br Assuming R R R the difference in distances

Assuming (R1+R2)≈2R, the difference in distances travelled is
The discrepancy in ΔR between the approximate and real cases is 2h1/R and can be neglected if it is much smaller than π. The concept of parallel rays is applicable if
Both SPLLS and EDCLLS are used in combination with a remote control station (RCS). In the former case the RCS is controlled by a human operator. This limits the transmission antenna height to 1.5–1.8m. In the latter case the RCS automatically changes parameters with time without the attention of a human operator. The height of the receiving antenna may reach 2.4m (standard ceiling height in a modern building). It follows from Fig. 1 that the tangent of the incidence angle θ is
The amplitudes of the reflected wave and direct wave depend on the distance difference (R2–R1) where
In the maximum points the function the distances to the maximums of the muscle metabolism pattern are equal to
In the minimum points the function the distances to the minima of the radiation pattern are equal to
In the case of h1≈h2, the following equations for the coordinates of the maxima and minima are used: where = 1, 2, … is the Fresnel\'s zone number. The calculation data obtained for radiation patterns of SPLLS and EDCLLS light sources are presented in Table 1. In addition to this data we obtained the value 2kh1/R1= 2.06, R ≫26m for SPLLS light source and for h1= 1.5m. Then, 2kh1/R1= 0.96, R ≫73.34m for EDCLLS light source, for h1= 1.5m and h2= 6.5m. In this case in many practical applications the concept of parallel rays is inapplicable. The relative amplitude of the reflected wave is described by reflection coefficients known in optics as Fresnel\'s coefficients. In the cases of horizontal, vertical and circular polarizations they are given by where Γ, Γ, Γ are the horizontal, vertical and circular polarization reflection coefficients, respectively; and η are the permittivity, the conductivity and the complex permittivity of the reflecting medium. The reflection coefficients are complex numbers meaning that during reflection not only the amplitude of the reflected wave changes but also its phase does. Assuming that both media have equal permeability = 1 and that one medium is a free space, the reflection coefficient depends only on the complex permittivity of the material. The complex permittivity of typical building materials, obtained experimentally [7], demonstrates significant variations from one material to another, while showing a little frequency dependence (see Table 2). The presence of the imaginary part of the complex electric permittivity is an evidence of the presence of electrical conductance. However, numerical estimation shows that the influence of the imaginary part of η can be neglected during calculations of the coefficients Γ and Γ. At the frequency of 2445MHz, the minimum of the first Fresnel\'s zone Rmin1= 58.68m, the incidence angle θ= 3.8°, the reflection coefficients , for , . Assuming , the reflection coefficients are , , thus the assumption of 0 does not produce significant errors. To calculate the range of a radio control link let us use the model [6] that accounts for the ground reflection. The same paper presents the experimental results validating the ground reflection model. The necessary formulae are the following: where θ is the incidence angle; R1, R2 are the direct and the reflected ray path lengths, respectively; Pdir trans, Pref trans are the power quantities of the direct and the reflected waves, respectively; Ptot, Ptot dBm are the total received power quantities in watts and in decibels above 1mW. It follows from Eqs. (6) and (7) given for Rmax and Rmin, that the smaller is the angle θ the farther from the geometrical point of reflection is the center of the Fresnel\'s zone, and the ellipse itself is longer and narrower. At a long distance the lowest, i.e., the first (n = 1) lobe of the radiation pattern is the most important. If the angle θ is equal to the angle of the ‘axis’ of this lobe then the lobe is closer to the ground. For the field at the receiving antenna to be consistent with the interference approach it is necessary for the reflecting ground surface to be smooth (with small disturbances) at least within the first Fresnel\'s zone. The disturbances outside the first Fresnel\'s zone have little influence. In optics [8] the disturbances (the deviations from a perfectly flat surface) of the surface of a reflecting mirror must not exceed λ/10 or even λ/16. These values correspond to the normal incidence and can be considered as limiting values. If the incidence is not normal then the influence of disturbances is decreased by a factor of sinθ, allowing for disturbance height